Four militants were killed in resurgent Israeli air strikes overnight as a short period of calm ended. Three were members of Hamas's military wing, the Ezzedin al-Qassam brigades, according to reports on its website.

Hamas, which normally distances itself from rocket fire from Gaza, has claimed responsibility for some operations in recent days. "These holy missions come in response to the repeated, continuous crimes of the enemy against our people, which killed four and injured 10 in the past 48 hours," it said in a statement.

Israel's defence minister, Ehud Barak, said he would order whatever action was necessary to stop rocket fire from Gaza. "If a ground operation will be necessary, there will be a ground operation. Nobody is eager for this but we will act as we are required to stop this wave and to increase the effectiveness of the operation."

Israeli tanks have fired into Gaza in addition to air strikes, according to reports. Schools in both southern Israel and central Gaza were closed on Wednesday, and the Israeli authorities shut crossing points to the enclave.

Both Israel and Hamas are thought to want to avoid an escalation into full-scale conflict. But if Israeli casualties resulted from rocket fire, Israel would be expected to engage in a more sustained assault than targeted assassinations.

Hamas is also under pressure from more radical organisations within Gaza, which may explain its unusual open participation in this latest round of violence. "Hamas feels a tension between the need to be a government [in Gaza] and the need to be part of the resistance [to Israel]. It has in its ranks quite a few people who co-operate with the more radical groups," Yossi Kuperwasser, the director general of Israel's ministry of strategic affairs, told reporters in a briefing last week.

Weapons were "pouring in" to Gaza, he added. "Everyone is extremely busy building a terror infrastructure. Libya is a new and very important source of weapons. The arming process is very intensive and with it comes a growing tendency to use such arms."

Earlier this month, an anti-aircraft missile was fired from Gaza for the first time at an Israeli military helicopter, according to Israeli defence officials. The shoulder-fired Strela missile missed its target.

The visit by the Qatari emir‚ the first head of state to visit Gaza under Hamas rule, was seen as conferring legitimacy on the Islamist organisation. Sheikh Hamad bin Khalifa Al Thani also announced a $400m investment and construction programme for Gaza.